The stock of Nogro Corporation is currently selling for $$10$ per share. Earnings per share in the coming year are expected to be $$2.$ The company has

a policy of paying out $50\%$ of its earnings each year in dividends. The rest

is retained and invested in projects that earn a $20\%$ rate of return per year.

This situation is expected to continue indefinitely.

a$.$ Assuming the current market price of the stock reflects its intrinsic

value as computed using the constant$-$growth DDM$,$ what rate of return

do Nogro$$s investors require?

b$.$ By how much does its value exceed what it would be if all earnings

were paid as dividends and nothing was reinvested?

c$.$ If Nogro were to cut its dividend payout ratio to $25\%,$ what would

happen to its stock price?

d$.$ What if Nogro eliminated the dividend?